Fast Langevin based algorithm for MCMC in high dimensions

2015/07/08 by Alain Durmus, Gareth O. Roberts, Durmus, Alain +5
Computer Science · Mathematics · #60F05 #65C05 #Bayesian Methods and Mixture Models #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Numerical Analysis (math.NA) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1507.02166

openalex publication_date 2015/07/08 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We introduce new Gaussian proposals to improve the efficiency of the standard Hastings-Metropolis algorithm in Markov chain Monte Carlo (MCMC) methods, used for the sampling from a target distribution in large dimension d. The improved complexity is O(d^1/5) compared to the complexity O(d^1/3) of the standard approach. We prove an asymptotic diffusion limit theorem and show that the relative efficiency of the algorithm can be characterised by its overall acceptance rate (with asymptotical value 0.704), independently of the target distribution. Numerical experiments confirm our theoretical findings.

Citations

• Monte Carlo sampling methods using Markov chains and their applications

Cited by

• Improving dynamical properties of metropolized discretizations of\n overdamped Langevin dynamics
• Optimal scaling of MCMC algorithms: the Hamiltonian approach

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